Re: Circles and ellipses

> Unfortunately, not everyone would agree. I think a circle has two
 coincident
> foci, and an ellipse with coincident foci is a circle.
>

You are right that not everyone would agree. You are also right that, if you take an ellipse, and allow its two foci to coincide, and call that two foci, you get a circle. Well, you get the same set of points as a circle, anyway.

Phlip is also right in pointing out how far afield this has gotten. So let me try to bring it back, just a little, closer to issues that surface with relational databases. If a single point can be construed as two coincident foci, than why can't two rows of a table have the same values, in all of the columns, and still be two elements of the relation the table is supposed to represent?

Of course, you can't do that... it's a violation of 1NF. Believe it or not, I've actually seen this problem surface in a real, actual relational DB in the field. The resulting confusion made it impossible to distinguish duplicate billing due to clerical error from a case where the same customer orders the same product twice in one day. I am not making this up. Not that this proves anything in the current discussion.

But let's return to cicle/ellipse for a minute? Why would anyone WANT to consider a circle an ellipse? Well, I can see one immediate benefit: if all the relevant operations that work on an ellipse also work on a circle, then you can get more useful software written by construing a cirlce as a specialized ellipse, and not writing an implementation for a whole different class.

That, to me, is more to the point than the underlying math.

--
Regards,
    David Cressey
    www.dcressey.com
"Bob Badour" <bbadour_at_golden.net> wrote in message
news:u4Ef7.75$ch5.18757673_at_radon.golden.net...


> >The entire discussion about whether a circle is an ellipse hinges on how


 you


> >define circle and ellipse.

> >

> >If you take the classical definition of an ellipse, from Euclidean


 geometry,


> >defined based on the sum of the distances from each point on the ellipse


 to


> >the two foci, then a circle is NOT an ellipse.  A circle does not have


 two


> >foci.

>

>

> For instance, if one stretches an ellipse such that the length of its

 major


> semiaxis equals the length of its minor semiaxis, the foci will shift such

> that they occupy the same point. Does the ellipse suddenly cease to be an

> ellipse when this happens? In what way does the resulting shape differ

 from


> a circle?

>

>

>